Two-variable linear pricing: The cost of 2 sarees and 4 shirts is ₹16,000, and the cost of 1 saree and 6 shirts is also ₹16,000. What is the total cost of 12 shirts (assume uniform prices)?

Introduction / Context:We are given two linear equations in two unknowns: the unit price of a saree and the unit price of a shirt. Solving them allows us to compute the specific cost requested for 12 shirts. This is a standard elimination/substitution exercise in linear equations applied to pricing.

Given Data / Assumptions:

• 2S + 4T = 16000 (S = saree price, T = shirt price)
• 1S + 6T = 16000
• Prices are uniform; no discounts or bundles implied.

Concept / Approach:Solve the system for S and T using elimination. Then multiply T by 12 to get the requested total. Keep arithmetic organized to avoid sign mistakes.

Step-by-Step Solution:

Verification / Alternative check:Check in (1): 2*4000 + 4*2000 = 8000 + 8000 = 16000 ✔; in (2): 4000 + 12000 = 16000 ✔.

Why Other Options Are Wrong:₹12,000 is for 6 shirts; ₹48,000 doubles the correct value; ₹18,000 assumes ₹1500 per shirt; “Cannot be determined” is incorrect because the system is solvable and consistent.

Common Pitfalls:Subtracting the wrong equation or mismatching coefficients often yields negative or nonsensical prices. Always verify by substitution.

Final Answer:₹ 24,000